2 citations · 4 across the 11 of their papers we have counts for
12 papers
Infinitely many hyperelliptic curves of small genus and small fixed rank, and of any genus and rank two
Stevan Gajović, Sun Woo Park
We prove that for any number field and any fixed genus , there are infinitely many non-isomorphic hyperelliptic curves of genus over whose Jacobians have rank…
Pythagoras numbers for infinite algebraic fields
Nicolas Daans, Stevan Gajović, Siu Hang Man +1
We prove that the Pythagoras number of the ring of integers of the compositum of all real quadratic fields is infinite. The same holds for certain infinite totally real cyclotomic…
The density of elliptic curves over with a rational 3-torsion point or a rational 3-isogeny
Stevan Gajović, Lazar Radičević, Matteo Verzobio
We determine the probability that a random Weierstrass equation with coefficients in the -adic integers defines an elliptic curve with a non-trivial -torsion point, or with a…
Arithmetic-geometric mean sequences over finite fields , where
Natália Bátorová, Stevan Gajović
Arithmetic-geometric mean sequences were already studied over real and complex numbers, and recently, Michael J. Griffin, Ken Ono, Neelam Saikia and Wei-Lun Tsai considered them ov…
Local-global principle for 11-isogenies of elliptic curves is true over quadratic fields
Stevan Gajović, Jeroen Hanselman, Angelos Koutsianas
In this paper, we prove that the local-global principle of -isogenies for elliptic curves over quadratic fields does not fail. This gives a positive answer to a conjecture by B…
On -adic denseness of quotients of values of integral forms
Deepa Antony, Rupam Barman, Stevan Gajović +1
Given , the ratio set or the quotient set of is defined by . It is an open problem to study the denseness of in the …
Computing p-adic heights on hyperelliptic curves
Stevan Gajović, J. Steffen Müller
We describe an algorithm to compute the local Coleman-Gross p-adic height at p on a hyperelliptic curve. Previously, this was only possible using an algorithm due to Balakrishnan a…
Linear quadratic Chabauty
Stevan Gajović, J. Steffen Müller
We present a new quadratic Chabauty method to compute the integral points on certain even degree hyperelliptic curves. Our approach relies on a nontrivial degree zero divisor suppo…
Reverse engineered Diophantine equations
Stevan Gajović
We answer a question of Samir Siksek, asked at the open problems session of the conference ``Rational Points 2022'', which, in a broader sense, can be viewed as a reverse engineeri…
Cubic and quartic points on modular curves using generalised symmetric Chabauty
Josha Box, Stevan Gajović, Pip Goodman
Answering a question of Zureick-Brown, we determine the cubic points on the modular curves for as well as the quartic points on . To…
The density of polynomials of degree over having exactly roots in
Manjul Bhargava, John Cremona, Tom Fisher +1
We determine the probability that a random polynomial of degree over has exactly roots in , and show that it is given by a rational function of…
Curves with sharp Chabauty-Coleman bound
Stevan Gajović
We construct curves of each genus for which Coleman's effective Chabauty bound is sharp and Coleman's theorem can be applied to determine rational points if the rank cond…